Answer:
We can use the following formula for the cosine of the sum of two angles:
cos(α + β) = cos(α)cos(β) - sin(α)sin(β)
To use this formula, we need to find the values of cos(α), sin(α), cos(β), and sin(β).
Since tan(α) = 4/3 and α is in the first quadrant, we can use the Pythagorean identity to find sin(α) and cos(α):
tan^2(α) + 1 = sec^2(α)
(4/3)^2 + 1 = sec^2(α)
16/9 + 1 = sec^2(α)
25/9 = sec^2(α)
sec(α) = 3/5
cos(α) = 1/sec(α) = 5/3
sin(α) = tan(α) * cos(α) = (4/3) * (5/3) = 20/9
Since cos(β) = -4/5 and β is in the third quadrant, we can use the Pythagorean identity again to find sin(β):
sin^2(β) + cos^2(β) = 1
sin^2(β) = 1 - cos^2(β)
sin(β) = -√(1 - cos^2(β)) (since sin(β) is negative in Q3)
sin(β) = -√(1 - (-4/5)^2) = -√(1 - 16/25) = -√(9/25) = -3/5
Now we can substitute these values into the formula for cos(α+β):
cos(α + β) = cos(α)cos(β) - sin(α)sin(β)
cos(α + β) = (5/3) * (-4/5) - (20/9) * (-3/5)
cos(α + β) = -4/3 + 4/3
cos(α + β) = 0
Therefore, cos(α+β) = 0.
residents of eastport are concerned about the number of drivers who speed when riving down main street a group of residents take turns observing the street each person spends one hour counting how many drivers speed and how obey the speed limit
Answer:in your mouth
Step-by-step explanation:
given list (10, 11, 12, 13, 14, 15), how many comparisons will be made during the third outer loop execution (i = 3)?
The third outer loop execution (i = 3), the loop compares the third element (12) with the remaining elements in the list (13, 14, 15) for a total of 3 comparisons
Assuming the outer loop is a standard loop that iterates through the list from the first to the second-to-last element, the number of comparisons made during the third outer loop execution (i = 3) would be 3.
During the first outer loop execution (i = 1), the loop compares the first element (10) with the rest of the elements in the list (11, 12, 13, 14, 15) for a total of 5 comparisons.
During the second outer loop execution (i = 2), the loop compares the second element (11) with the remaining elements in the list (12, 13, 14, 15) for a total of 4 comparisons.
During the third outer loop execution (i = 3), the loop compares the third element (12) with the remaining elements in the list (13, 14, 15) for a total of 3 comparisons.
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Assuming you are using a standard bubble sort algorithm, during the third outer loop execution (i = 3), there will be 3 comparisons made.
The given list (10, 11, 12, 13, 14, 15) and the number of comparisons made during the third outer loop execution (i = 3):
In the first outer loop iteration (i = 1), there will be 5 comparisons (comparing elements at positions 1-2, 2-3, 3-4, 4-5, and 5-6).
In the second outer loop iteration (i = 2), there will be 4 comparisons (comparing elements at positions 1-2, 2-3, 3-4, and 4-5).
In the third outer loop iteration (i = 3), there will be 3 comparisons (comparing elements at positions 1-2, 2-3, and 3-4).
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Kalani has a savings account and a checking account. For one year she deposited x dollars into her checking account every week and y dollars into her savings account every month. Each checking account deposit was half the amount of each savings account deposit, and the total of all deposits for the year was $15,200. Which system of equations can be used to determine the values of x and y?
Kalani deposited $200 into her checking account every week and $400 into her savings account every month.
What is system of equation?A group of equations that must be solved simultaneously is referred to as a system of equations. Typically, a system of equations involves multiple variables, and the goal is to find the values of those variables that satisfy all of the equations in the system.
According to question:Let's start by using the given information to write equations for the total amount deposited in each account over the course of the year.
For the checking account, Kalani deposited x dollars every week for 52 weeks, so the total amount deposited for the year is:
52x
For the savings account, Kalani deposited y dollars every month for 12 months, so the total amount deposited for the year is:
12y
We are also told that each checking account deposit was half the amount of each savings account deposit, so we can write:
x = (1/2)y
Finally, we are given that the total of all deposits for the year was $15,200, so we can write:
52x + 12y = 15200
A system of two equations with two variables is now available:
x = (1/2)y
52x + 12y = 15200
We can solve this system to determine the values of x and y. The result of putting the first equation into the second equation is:
52(1/2)y + 12y = 15200
Simplifying:
26y + 12y = 15200
38y = 15200
y = 400
Substituting y = 400 into the first equation, we get:
x = (1/2)y = (1/2)(400) = 200
Therefore, Kalani deposited $200 into her checking account every week and $400 into her savings account every month.
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dont understand what m supposed to do at the radius = diameter/2 part
Step-by-step explanation:
Radius simply means half of the diameter. In other words radius is the distance between the center of the circle to the outside of the circle
. a fair coin is flipped 8 times and thesequence of heads and tails is noted. in howmany outcomes are therea. exactly 6 heads?b. at least 3 heads?c. at most 6 heads?d. at most 2 head
The total number of possible outcomes when flipping a coin 8 times is 2^8 = 256.
a. To get exactly 6 heads, we need to choose 6 out of the 8 flips to be heads, and the remaining 2 flips to be tails. The number of ways to choose 6 out of 8 is given by the binomial coefficient (8 choose 6) = 28. Therefore, there are 28 possible outcomes with exactly 6 heads.
b. To get at least 3 heads, we need to count the number of outcomes with 3, 4, 5, 6, 7, or 8 heads. Using the same logic as part (a), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at least 3 heads.
Number of outcomes with 3 heads: (8 choose 3) = 56
Number of outcomes with 4 heads: (8 choose 4) = 70
Number of outcomes with 5 heads: (8 choose 5) = 56
Number of outcomes with 6 heads: (8 choose 6) = 28
Number of outcomes with 7 heads: (8 choose 7) = 8
Number of outcomes with 8 heads: (8 choose 8) = 1
Total number of outcomes with at least 3 heads = 56 + 70 + 56 + 28 + 8 + 1 = 219.
c. To get at most 6 heads, we need to count the number of outcomes with 0, 1, 2, 3, 4, 5, or 6 heads. Using the same logic as part (b), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at most 6 heads.
Number of outcomes with 0 heads: (8 choose 0) = 1
Number of outcomes with 1 head: (8 choose 1) = 8
Number of outcomes with 2 heads: (8 choose 2) = 28
Number of outcomes with 3 heads: (8 choose 3) = 56
Number of outcomes with 4 heads: (8 choose 4) = 70
Number of outcomes with 5 heads: (8 choose 5) = 56
Number of outcomes with 6 heads: (8 choose 6) = 28
Total number of outcomes with at most 6 heads = 1 + 8 + 28 + 56 + 70 + 56 + 28 = 247.
d. To get at most 2 heads, we need to count the number of outcomes with 0, 1, or 2 heads. Using the same logic as parts (b) and (c), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at most 2 heads.
Number of outcomes with 0 heads: (8 choose 0) = 1
Number of outcomes with 1 head: (8 choose 1) = 8
Number of outcomes with 2 heads: (8 choose 2) = 28
Total number of outcomes with at most 2 heads = 1 + 8 + 28 = 37.
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Solve and simplify your answer.
6/7 + 1/8
Answer: 41/56
Step-by-step explanation:
first you would try to find a common denominator (or LCM) in this case, its 56 so the revised question is 48/56+7/56 because you have to change the numerator as well. if you subtract the numerators it is 41. so its 41/56. 41/56 is already in its simplest form, so the answer is 41/56
{1, 2, 3,..., 175, 176, 177, 178}
How many numbers in the set above
have 5 as a factor but do not have
6-10 as a factor?
A. 1
B.
3
C. 4
D. 17
E. 18
Answer:
I'm guessing A
Step-by-step explanation:
175 is the only multiple of 5 so it has to be that also there's no option for zero
If a student pulls out a jellybean without looking what is the probability that the jellybean will be yellow? 5/11 probability practice
What is the equation of the line that is perpendicular to the given line and passes through the point (2, -2) and is perpendicular to the line represented by y=2/5x+2?
The equation of line passes through the point (2, -2) and is perpendicular to the line represented by y=2/5x+2 is y = -5x/2+3
Given that a line is passing through the point (2, -2) and is perpendicular to the line y = 2x/5+2, we need to find the equation of the line,
The equation of line is, y = mx + c, where m is the slope,
So, we know that the slopes of the perpendicular lines are negative reciprocal of each other,
So, the slope of the required line is -5/2.
Therefore, the equation will be
y = -5x/2 +c
To find c put x = 2, y = -2
-2 = -5(2)/2 + c
-2 = -5 + c
c =3
Hence, the equation is, y = -5x/2+3
Therefore, the equation of line passes through the point (2, -2) and is perpendicular to the line represented by y=2/5x+2 is y = -5x/2+3
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Quiz Active
Does anyone know the answer
The equation of the circle is (x + 1)² + (y - 1)² = 16.
option D
What is the equation of the circle?
The radius of the circle is 4, and the center of the circle is (-1, 1).
The equation of a circle with center (a,b) and radius r is given by:
(x - a)² + (y - b)^2 = r²
In this case, the center of the circle is (-1, 1) and the radius is 4. Plugging these values into the equation, we get:
(x - (-1))² + (y - 1)² = 4²
Simplifying the equation, we get:
(x + 1)² + (y - 1)² = 16
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May you please help me
Line JN = line AE = 22ft
Line DC = Line LM = 17ft
Line KL = line BC = 12 ft
< D = <M = 158°
< K = <B = 135°
What are congruent shape?Two shapes are said to be congruent when they both have the same length size and same angle measurements.
From the given shapes, polygon ABCDE = JKLMN.
Therefore the corresponding angles and lengths is as follows:
Line JN = line AE = 22ft
Line DC = Line LM = 17ft
Line KL = line BC = 12 ft
< D = <M = 158°
< K = <B = 135°
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Can someone show me step by step on how to do this
An image of a rhombus is shown.
a rhombus with a base of 16 centimeters and a height of 14 centimeters
What is the area of the rhombus?
224 cm2
120 cm2
112 cm2
60 cm2
Select the correct answer.
The graph of function f is shown.
Function g is represented by the equation.
g(x) = 4(1/4)^x +2
Which statement correctly compares the two functions?
A. They have different y-intercepts but the same end behavior.
B. They have different y-intercepts and different end behavior.
C. They have the same y-intercept and the same end behavior.
D. They have the same y-intercept but different end behavior.
Answer:
A. They have different y-intercepts but the same end behavior.
Step-by-step explanation:
From the shape of f we see that its a descending exponential fnction, so the factor taken to the power x will be a fraction, and from the points the eqation is
f(x) = 2(1/4)^x + 2
and the y-intercept is 4
g(x) has y-intercept of 4(1/4)^0 + 2 = 6 so they are different.
As x approaches infinity both f and g approach 2 so the end behavior s the same.
can someone show me step by step only and correctly
A cylinder has the net shown.
net of a cylinder with diameter of each circle labeled 3.8 inches and a rectangle with a height labeled 3 inches
What is the surface area of the cylinder in terms of π?
40.28π in2
22.80π in2
18.62π in2
15.01π in2
Answer:
18.62π square inches
Step-by-step explanation:
To find the surface area of the cylinder, we need to find the area of each of its components and add them together. We can use the net of the cylinder to visualize its components and dimensions.
First, let's find the area of the top and bottom circles. We know the diameter of each circle is 3.8 inches, so the radius is half of that, or 1.9 inches. The formula for the area of a circle is A = πr^2, so:
A(top and bottom circles) = 2π(1.9 in)^2
= 2π(3.61 in^2)
= 7.22π in^2
Next, let's find the area of the curved surface of the cylinder. The height of the cylinder is labeled as 3 inches, which is also the height of the rectangle in the net. The length of the rectangle is the circumference of one of the circles, which is πd (where d is the diameter). So:
length of rectangle = π(3.8 in) = 11.96 in
The formula for the area of the curved surface of a cylinder is A = 2πrh, where r is the radius and h is the height. We can use the radius we found earlier and the height of 3 inches to calculate the area of the curved surface:
A(curved surface) = 2π(1.9 in)(3 in)
= 11.4π in^2
Finally, we can add the areas of the top and bottom circles and the curved surface to get the total surface area of the cylinder:
Total surface area = A(top and bottom circles) + A(curved surface)
= 7.22π in^2 + 11.4π in^2
= 18.62π in^2
Therefore, the surface area of the cylinder in terms of π is 18.62π square inches.
Solve for x. Round your answer to the nearest tenth and type it in the blank without "x=".
Answer:
2.66 round 2.7
Step-by-step explanation:
the triangles are similar, therefore with the measures in proportion
6 : 8 = 2 : x
x = 2 x 8 : 6
x = 16 : 6
x = 2.66 round 2.7
i need help please help me
You can take a look at this, the image that I attached might help.
For example, the first one shifts left because the h value is positive 3. -(3) = -3.
Calvin has a gift card which he is using to buy candy (x), and he has been tracking how much money (y) he spends. He noted that after buying 4 pieces of candy (in all) he has $28.00 left on his card and then after buying 10 pieces of candy (in all) he has $25.00 left on his card. Write the equation of the line that represents his spending on candy
Answer:
To write the equation of the line that represents Calvin’s spending on candy, we need to first find the slope and the y-intercept of the line.
We can use the two points given in the problem: (4, 28) and (10, 25)
Slope (m) = (y2 - y1) / (x2 - x1)
= (25 - 28) / (10 - 4)
= -3/6
= -1/2
The slope represents the rate at which Calvin is spending money on candy.
Now, we can use the point-slope form of the equation of a line to find the equation of the line.
y - y1 = m(x - x1)
y - 28 = (-1/2)(x - 4)
y - 28 = (-1/2)x + 2
y = (-1/2)x + 30
Therefore, the equation of the line that represents Calvin’s spending on candy is y = (-1/2)x + 30.
Answer: Equation that represents his spending on candy- y = (³⁄₁₀) x
X = number of candy
Step-by-step explanation:
y = money spend x = number of candy
y = (m)x
cost for 10 pieces of candy = $(28 - 25) = $3
⇛ 3 = (m)x10 (x = 10 & y = 3)
⇛m=(³⁄₁₀)
Therefore the equation representing his spending on candy is
⇛ y = (³⁄₁₀) x
Kendie's family usually pays $36 for admission to the planetarium. On Sundays visitors receive a discount of 1/6 off the total admission price.
How much would Kendie's family pay to visit the planetarium on Sunday?
fraction diagram needed.
As a result, they would pay: 5/6 x $36 = $30 as Kendie's family would shell out 1/6 less than the standard admission price.
what is unitary method ?In mathematics, the linear approach is a way when resolving issues with direct or negative proportion. It entails figuring out the value of one unit of a quantity and utilising that value to figure out the value of any given quantity divided by that number of units. For instance, using the unitary technique, if we know that 5 oranges cost $10, we may calculate the price of 10 apples by first dividing $5 by 5 to get $2 per apple, multiplying $two by 10 to get $20 for 10 apples, and then using the result to get the price of 5 apples. In industries where proportional correlations are regularly found, like banking, business, and science, the unitary technique is frequently employed.
given
On Sunday, Kendie's family would shell out 1/6 less than the standard admission price, or 5/6 of the standard admission price.
As a result, they would pay: 5/6 x $36 = $30 as Kendie's family would shell out 1/6 less than the standard admission price.
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Your friend says that the inequalities x ≤ 4/3 and -6x ≤ -8 is your friend correct? Explain
x - 4/3 ≤ 0 is equivalent to x ≥ 4/3, and they both represent the same set of values for x. My friend is correct.
Are the inequalities x ≤ 4/3 and -6x ≤ -8 equivalent?The relationship between two values that are not equal is defined by inequalities.
When we subtract 4/3 from both sides; x ≤ 4/3 can be rewritten as:
x - 4/3 ≤ 0
-6x ≤ -8 can be simplified by dividing both sides by -6 and reversing the inequality which gives:
x ≥ 4/3.
Full question "Your friend says that the inequalities x ≤ 4/3 and -6x ≤ -8 is your friend correct? Explain the reason"
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Jenae wants to buy a fuel-efficient car. She finds one that can travel 500 miles on one tank of gas. If the gas tank holds 16 gallons, calculate the miles per gallon.
20PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED AND PLS PLS PLS EXPLAIN THE ANSWER OR HOW U GOT IT PLEASE AND TY
Required value of cosy is 12/13.
What is Complementary angle?
Two angles are said to be complementary if their addition is 90°.Let if one angle is x then the other angle will be 90° – x. Hence, we use these complementary angles for trigonometry ratios, where one ratio is complementary to another ratio by 90 degrees such as,
[tex]sin(x) = \cos(\frac{\pi}{2} - x) \\ \tan(x) = \cot(\frac{\pi}{2} - x) \\ \sec(x) = \csc(\frac{\pi}{2} - x) \\ \cos(x) = \sin(\frac{\pi}{2} - x) \\ \cot(x) = \tan(\frac{\pi}{2} - x) \\ \csc(x) = \sec(\frac{\pi}{2} - x)[/tex]
Given, here x and y are complementary.
So, we can say that
[tex]x + y = {90}^{o} \\ y = {90}^{o} - x[/tex]
So,
[tex] \sin( x) = \frac{12}{13} \\ \sin( {90}^{o} - y) = \frac{12}{13} \\ \cos(y) = \frac{12}{13} [/tex]
Therefore, required value of cosy is 12/13.
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a band just recorded a new album with 13 tracks. the shortest song on the album is 1 minute and 14 seconds. The longest song is 5 minutes and 54 seconds. What is a reasonable estimate for the total time of the album?
To find a reasonable estimate for the total time of the album, we can add the times of the shortest and longest songs and divide by 2 to find the average time per song, and then multiply by the total number of songs on the album.
What is a reasonable estimate for the total time of the album?The shortest song on the album is 1 minute and 14 seconds, which is equivalent to 74 seconds.
The longest song on the album is 5 minutes and 54 seconds, which is equivalent to 354 seconds.
Therefore, the average time per song is:
(74 + 354) / 2 = 214 seconds
And the total time of the album is approximately:
13 songs x 214 seconds/song = 2,782 seconds
Converting this to minutes and seconds, we get:
2,782 seconds = 46 minutes and 22 seconds
So a reasonable estimate for the total time of the album is about 46 minutes and 22 seconds.
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One baseball team played 15 games throughout the season. If this baseball team won 9 of those games, what percent of the games did they win?
Answer:
The baseball team won 60% of the games they played.
Step-by-step explanation:
To find the percentage of games the baseball team won, we can use the following formula:
percentage = (wins / total games) x 100
where wins is the number of games won and total games is the total number of games played.
Substituting the given values, we get:
percentage = (9 / 15) x 100
percentage = 0.6 x 100
percentage = 60%
Therefore, the baseball team won 60% of the games they played.
Answer:
60%
Step-by-step explanation:
9 out of 15, written in *fraction form* is 9/15, when reduced down, 9/15 becomes 3/5. When you insert 3/5 into a calculator you get 0.6 . Since percentage is based off a x/100, you move the decimal point of 0.6 over 2 units to the right, you get 60, so it would in final would be 60/100 which equals 60%
* ( Ex. 1 out of 3 = 1/3 )
Happy Mathing <3
-J
Solve the system using elimination -6X = 18 - Y 9 = -3X - 8Y
The solution to the system by elimination is (-2, 4).
Solving the system using eliminationTo solve the system using elimination, we need to eliminate one of the variables by multiplying one or both of the equations by a constant.
-6X = 18 - Y
9 = -3X - 8Y
Rewrite as
-6X = 18 - Y
3X = 9 - 8Y
So, we have
-6X = 18 - Y
6X = 18 - 8Y
Now we can add this equations to the second equation to eliminate x:
0 = 36 - 9Y
This gives
9Y = 36
So, we have
Y = 4
Recall that
-6X = 18 - Y
So, we have
-6X = 18 - 4
So, we have
-6X = 12
Divide by 2
X = -2
Therefore, the solution to the system is (-2, 4).
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
The drive-thru that typically has more wait time is
Burger Quick, because it has a larger median.
Option A is correct.
How do we calculate?Because Burger Quick's box plot displays a higher interquartile range (from 9.5 to 24) than Super Fast Food (from 8.5 to 15.5), Burger Quick often has longer wait times.
Additionally, Burger Quick's median (15.5) is greater than Super Fast Food's median (12), demonstrating that Burger Quick's middle value of reported wait times is higher than Super Fast Food's middle value of reported wait times.
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Write down the size of angle ABC. Give a reason for your answer.
Answer:
∠ ABC = 90°
Step-by-step explanation:
∠ ABC is the angle on the circle subtended by the diameter AC
it is the angle in a semicircle and is 90°
what two numbers multiply to 21 and add to -10
Answer: brainliest ?
-3 and -7
Step-by-step explanation:
state the modal numbers
1,2,3,4,5,6,7
Answer:
there is no Modal number because all the numbers appears only once
imma be giving brainliest if you help me!!!???!!??
using trignometric ratio of sine thee measure of the angle x to the nearest degree is 28 degrees
What is Trignometric ratio?Trigonometric ratios are ratios of the sides of a right triangle, such as sine, cosine, and tangent, that are used to find missing side lengths or angles.
What is angle?An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. It is typically measured in degrees or radians.
According the given information:
We can use the trigonometric ratio of sine to find the measure of the angle x.
sin(x) = opposite/hypotenuse
In this case, the opposite side is the height of the triangle, which is 13, and the hypotenuse is the length of the diagonal line connecting the base and the top of the triangle. We can use the Pythagorean theorem to find the length of the hypotenuse.
hypotenuse² = base² + height²
hypotenuse² = 22² + 13²
hypotenuse² = 769
hypotenuse ≈ 27.73
Now we can substitute the values into the sine ratio:
sin(x) = 13/27.73
x ≈ 28 degrees
Therefore, the measure of the angle x to the nearest degree is 28 degrees.
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A-One Talent Agency has 109 clients. 46 of the clients play piano and 58 of the clients play guitar. 17 clients play both the piano and the guitar. How many of the clients do not play either instrument?
Number of clients who do not play either the piano or the guitar is 22
To find the number of clients who do not play either instrument, we need to subtract the number of clients who play either the piano or the guitar or both from the total number of clients.
Let A be the set of clients who play the piano, and B be the set of clients who play the guitar. Then, we can use the formula A union B
|A ∪ B| = |A| + |B| - |A ∩ B|
where |A ∪ B| is the number of clients who play either the piano or the guitar or both, |A| is the number of clients who play the piano, |B| is the number of clients who play the guitar, and |A ∩ B| is the number of clients who play both instruments
Substituting the given values, we get
|A ∪ B| = 46 + 58 - 17
|A ∪ B| = 87
Therefore, the number of clients who do not play either instrument is:
109 - 87 = 22
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